Dynamic full three dimensional display

ABSTRACT

There is provided an optical system, including a light source, a control unit, and at least one juxtaposed double grating element, including a first grating and a second grating having grating functions, the gratings being spaced apart at a constant distance from each other, each of the two gratings having a center and at least one edge and comprising at least one sequence of a plurality of lines, wherein the spacing between the lines gradually changes from the center of the grating to the edges, the sequence of the plurality of lines of at least one of the gratings has a radial symmetry, and wherein the first grating diffracts a light wave from the light source towards the second grating and is further diffracted by the second grating as an output light wave in a given direction.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.15/999,301, filed Aug. 17, 2018 for “DYNAMIC FULL THREE DIMENSIONALDISPLAY”, which is hereby incorporated by reference herein.

FIELD OF THE INVENTION

The present invention relates to novel dynamic display sources, andparticularly to displays which perform operations that cannot beperformed by currently available technologies.

The invention can be implemented to advantage in a large number ofimaging applications, such as, dynamic full three-dimensional displays,compact and high-efficient micro-displays, Fourier transform lenslessdisplays, as well as non-imaging applications, such as backlightillumination for color-sequential displays.

BACKGROUND OF THE INVENTION

One of the most desired and sought after devices in the rapidlyexpanding market of consumer electronics is a dynamic realthree-dimensional display, namely, the required device should be adisplay which is capable of projecting into the eyes of a viewer adynamic three dimensional display with full color, high resolution andexceptional performance. Presently, there are numerous technologiesachieving stereoscopic displays, which provide simultaneously differentimages to the viewer's left and right eyes. As a result, the viewer hasthe illusion of looking at a stereoscopic object. These technologiesinclude Head-Mounted Displays (HMDs), anaglyph, polarization-baseddisplays, eclipse method, interference filters technologies and others.The main drawback of this family of displays is that only two points ofview from the object are projected into the viewer's eye and the imageis not sensitive to the movements of the head or the viewer's eyes. Inaddition, usually another external accessory, such as a pair ofspecially dedicated eyeglasses, is required to fully achieve thestereoscopic display.

The strive for a display having the capability of projecting a full, aswell as dynamic three-dimensional image to the viewer's eyes, has led toseveral different complex optical solutions, including: volumetric,holographic and integral displays, all of which are either not reallydynamic, or alternatively, fail to project a full three-dimensionaldisplay. Furthermore, these technologies can be usually effected onlyfor comparatively small or medium devices. As a result, there iscurrently no existing technology that can supply a real dynamic, as wellas full three-dimensional display, on wide screens having satisfactoryperformance.

The teachings included in U.S. Pat. Nos. 7,460,302 and 8,811,823, bothin the name of Applicant, are herein incorporated by references.

DISCLOSURE OF THE INVENTION

The present invention facilitates the design and fabrication of a newfamily of displays for, amongst other applications, dynamic fullthree-dimensional displays. The invention allows high performance andfull color even for large screen displays. The optical system offered bythe present invention is particularly advantageous because it can supplydisplays having unique characteristics which cannot be found in thestate-of-the-art implementations, and yet it can readily be incorporatedeven into optical systems having specialized configurations, utilizingobtainable fabrication techniques.

A further object of the present invention is to provide a compact, highefficient and back-illuminated micro-display. In today's micro-displaysmarket, the devices are Processing (DLP) (which complicates the eitherfront-illuminated such as Liquid Crystal on Silicone (LCoS) and DigitalLight optical design of the system), or of very low efficiency, such asa liquid Crystal Display (LCD). Other micro-display sources sufferinherently from low achievable maximal brightness. The present inventionenables a micro-display system having a simple back-illuminationapproach, a potential for a high efficiency and practically unlimitedmaximal brightness.

It is a further object of the invention to provide a relativelyinexpensive and simple Fourier-transform display, namely, a displaywherein each of the points in the projected display is presented bycollimated light waves, instead of a diverging light wave from asingular pixel, as is the case in conventional displays. This kind ofdisplay is particularly advantageous for optical systems, such as HMDs,wherein a collimated image is required. Utilizing a Fourier-transformdisplay, instead of a conventional display, will avoid the requirementfor a complicated and cumbersome collimating module.

It is a still further object of the invention to provide a novelillumination method for color-sequential display, wherein the back lightefficiently illuminates the red, green and blue (RGB) color subpixels,without the necessity for decreasing the brightness of the system by afactor of three, using the color filters in front of the subpixels.

A broad object of the present invention is therefore to alleviate thedrawbacks of state-of-the-art compact optical display devices and toprovide other optical components and systems having improvedperformance, according to specific requirements.

In accordance with the present invention there is therefore provided anoptical display system comprising a light source, a control unit, and anarray of at least two juxtaposed double grating elements, each of theelements comprising a first grating and a second grating, spaced apartat a constant distance from each other, each of the two gratings havingat least two edges and comprises at least one sequence of a plurality oflines, wherein the spacing between the lines gradually changes from oneedge of the grating to the other edge, and wherein the first gratingdiffracts a light wave from the light source towards the second gratingand is further diffracted by the second grating as an output light wavein a given direction.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described in connection with certain preferredembodiments, with reference to the following illustrative figures sothat it may be more fully understood.

With specific reference to the figures in detail, it is stressed thatthe particulars shown are by way of example and for purposes ofillustrative discussion of the preferred embodiments of the presentinvention only, and are presented in the cause of providing what isbelieved to be the most useful and readily understood description of theprinciples and conceptual aspects of the invention. In this regard, noattempt is made to show structural details of the invention in moredetail than is necessary for a fundamental understanding of theinvention. The description taken with the drawings are to serve asdirection to those skilled in the art as to how the several forms of theinvention may be embodied in practice.

In the drawings:

FIGS. 1A, 1B and 1C are diagrams illustrating arrangements of a doublegrating element, wherein one of the gratings can be laterallytranslated;

FIGS. 2A, 2B and 2C are diagrams illustrating another arrangement of adouble grating element, wherein the refractive index of substratebetween the gratings is dynamically, externally controlled;

FIGS. 3A, and 3B are diagrams illustrating yet another arrangement of adouble grating element, wherein a third, rotatable grating is positionednext to one of the gratings, in accordance with the present invention;

FIG. 4 is diagram illustrating an array of double grating elements, inaccordance with the present invention;

FIGS. 5A and 5B are diagrams illustrating an array of double gratingelements capable of performing two-dimensional scanning of output beams,in accordance with the present invention;

FIGS. 6A, and 6B are diagrams illustrating yet another arrangement of adouble grating element having rotational symmetry capable of performingtwo-dimensional scanning of an output beam, in accordance with thepresent invention;

FIG. 7 is a diagram schematically illustrating a side view of a doublegrating element having rotational symmetry, in accordance with thepresent invention;

FIGS. 8A, 8B and 8C are diagrams illustrating an arrangement of a doublegrating element, for separating an input light waves into threelaterally displaced output light waves having three different colors, inaccordance with the present invention;

FIGS. 9A and 9B are diagrams illustrating a double grating elementilluminating (a) a pixel of Liquid Crystal Display and (b) a pixel of aLiquid Crystal on Silicone, in accordance with the present invention;

FIGS. 10A, 10B and 10C are diagrams illustrating double grating elementsilluminating pixels of a Liquid Crystal on Silicone, in accordance withthe present invention;

FIGS. 11A and 11B are diagrams illustrating an array of double gratingelements forming a bi-state dynamic display, in accordance with thepresent invention;

FIG. 12 is a diagram schematically illustrating a conventional displaysource;

FIG. 13 is a diagram schematically illustrating an array of doublegrating elements forming a stereoscopic display, in accordance with thepresent invention;

FIGS. 14 and 15 are diagrams illustrating an array of double gratingelements forming a three-dimensional dynamic display, in accordance withthe present invention;

FIGS. 16A and 16B are prior art diagrams illustrating (a) the recordingand (b) the reconstructing processes of a holographic display;

FIG. 17 is a diagram schematically illustrating an array of doublegrating elements forming a full three dimensional display, in accordancewith the present invention;

FIGS. 18A and 18B are diagrams schematically illustrating a top view(18A) and front view (18B) of an eyeball tracking unit, comprising anemitter and a detector installed at the central top position of a frameof a display module, in accordance with the present invention;

FIG. 19 is a diagram illustrating an array of double grating elementsforming a multi-state dynamic display, wherein the emitted light wavesare deviated into the viewer's eyes, in accordance with the presentinvention;

FIG. 20 is a diagram illustrating an array of double grating elementsforming a three-dimensional dynamic display which simultaneouslyprojects different images to different viewers, in accordance with thepresent invention, and

FIGS. 21A and 21B are diagrams schematically illustrating an array ofdouble grating elements forming a full three dimensional display,wherein an eyeball tracking unit is located on the frame of the displayand measures the position and gaze direction of the viewer's eyes, inaccordance with the present invention.

DETAILED DESCRIPTION

There are many types of display systems currently being utilized in theconsumer market, as well as in the professional and military markets.Usually, all of these display systems are composed of a two-dimensionalarray of pixels, wherein each pixel emits a sequence of diverging lightwaves, where the amplitude and the color of each diverging light wave isdetermined by an electronic video signal which is fed into the controlmodule of the display. The object of the present invention is to devisea new family of display systems, wherein the output from each pixel isnot a diverging wave, as in conventional displays, but rather adirectional light wave, wherein not only the color and the amplitude arecontrolled by the video signal, but also the direction of the outputlight wave. That is to say, the video signal which is fed into thedisplay contains not only information about the color and the amplitudethat each pixel should emit at each time frame, but also the directionof the light wave which is emitted from each pixel. Therefore, a specialmechanism, which also controls the direction of the output beam fromeach pixel in the display, is illustrated herein.

The main building block of the pixels in the present invention is aDouble-Grating Element (DGE), comprising a pair of two differentgratings located at a constant distance from each other. These gratingshave two different pre-defined chirped grating functions, respectively,namely, there is a lateral variation in the grating period, such thatthe direction of the light waves illuminating the first grating beingdiffracted into the second grating and then diffracted out of the DGE,can be electronically controlled by various alternative methods. Oneapproach, shown in FIG. 1A, is based on two parallel gratings, G₁(x) andG₂(ξ), having grating functions {right arrow over (G₁)}(x,y) and {rightarrow over (G₂)}(ξ, η), respectively (hereinafter the lateralcoordinates of the two gratings G₁ and G₂ of the DGE will be (x,y) and(ξ, η), respectively). The distance D between the gratings is constant,and the input light wave impinging on the first grating, G₁(x), isnormal to the grating plane. As shown in FIG. 1B, with no translation ofone grating, the output light wave emerges from the second grating,G₂(ξ), in a normal direction to the grating plane. As illustrated inFIG. 1C, however, when G₁(x) is translated in a rightward direction byδx, the light rays from G₁(x) that intersect with the second gratingsG₂(ξ), impinge on points where the grating function is higher than thepoints that they impinged on before the translation. As a result, theoutput light wave is deviated by an angle φ, where the deviation ratio,k=D(sin φ)/δx, is a constant. Hence, a continuous linear translation ofG₁(x) induces a continuous angular steering of the output light wave.The detailed calculation of the required grating functions {right arrowover (G₁)}(x,y) and {right arrow over (G₂)}(ξ, η), fulfilling therequirement that the deviation angle φ, for a given translation δx, willbe a constant over the entire surface of the DGE, and can be found inthe references quoted above. One of the main advantages of this approachis that a very large deviation coefficient can be attained with thisDGE, so that, for example, with a minute linear translation of a fewtenths of a micron, it is possible to significantly change the directionof the output beam. As a result, the translation of the grating can beaccomplished with a small piezo-electric crystal, and there is no needfor a complicated translating or rotating mechanism.

An alternative method for controlling the direction of the output lightwave is illustrated in FIGS. 2A, 2B and 2C. As shown in FIG. 2A, the twogratings G₁(x) and G₂(ξ) are formed on a light-transmitting substrate onthe two parallel surfaces 6 and 8, respectively, of a light-transmittingsubstrate 4. A monochromatic plane wave W_(i) is coupled inside thesubstrate by the first grating G₁(x), and thereafter, coupled out by thesecond grating G₂(ξ). The refractive index of the substrate can bedynamically controlled by external means, including, but not limited to,applying an electric field to the substrate, or by illumination with astrong short-wavelength light source. As illustrated in FIGS. 2B and 2C,a change in the refractive index of the substrate yields an angulardeviation of the output light wave, namely, when the refractive index isv₁, the output light wave W_(o) emerges from the second grating G₂(ξ) atan angle φ₁ with respect to the substrate plane (FIG. 2B). When therefractive index is, however, changed to v₂ (wherein v₂<v₁), the raysthat are diffracted from the first grating G₁(x) into the second gratingG₂(ξ) at higher diffraction angles, due to the decrease in therefractive index of the substrate (FIG. 2C). As a result, the light raysfrom G₁(x) that intersect with the second gratings G₂(ξ) now impinge onpoints where the grating function is lower than the points they impingedon before modifying the refractive index. Consequently, the output lightwave W_(o) is deviated by an angle Δφ, namely, the output light waveemerges from grating G₂(ξ) at a different angle φ₂=φ₁−Δφ to thesubstrate plane (FIG. 2C), where Δφ is the deviation angle. Hence, acontinuous change in the refractive index induces a continuous angularsteering of the output light wave. The detailed calculation of therequired grating functions {right arrow over (G₁)}(x,y) and {right arrowover (G₂)}(ξ, η), fulfilling the requirement that the deviation angle Δφfor a given refractive index modification Δv will be a constant over theentire surface of the DGE, can be found in the references quoted above.

An alternative method, not described in the prior art, for achieving therequired angular steering of an output beam using a DGE, is illustratedin FIG. 3. A grating G₀, having at least one major axis, is positionedin front of the first grating G₁(x) wherein, as illustrated in FIG. 3A,at the default position, the two gratings are parallel to each other andthe input light wave W_(i) impinges on G₀ at an incident angle −θ(hereinafter, rotation angles counterclockwise and clockwise will bedenoted as positive and negative angles, respectively). The direction ofthe image light wave that is diffracted from G₀ is:sin α_(i) ⁰ =λG _(0x)−sin θ,  (1)where, G_(0x) is the x-component of {right arrow over (G₀)}(x,y,z), thereciprocal grating function of the grating G₀, the super script 0denotes that the image angle sin α_(i) ⁰ is related to the grating G₀and λ is the wavelength of the light wave. It is assumed that thegrating function of G₀ is

$\begin{matrix}{{{\overset{\rightarrow}{G_{0}}\left( {x,y,\ z} \right)} = \left( {\frac{\sin\theta}{\lambda},\ 0,0} \right)},} & (2)\end{matrix}$namely, G₀ is a linear grating having a constant lines period along thex axis. Inserting Eq. (2) into Eq. (1) yieldssin α_(i) ⁰=0.  (3)

That is, the image light wave is normal to the grating plane. Assumingnow that the grating G₀ is rotated counterclockwise around the y-axis byan angle δ, the reconstructing angle of the incoming light wave comparedto the rotated grating is:sin α′_(c) ⁰(δ)=sin(−θ−δ).  (4)

The output angle of the image wave is:sin α′_(i) ⁰(δ)=λG _(0x)+sin α′_(c) ⁰(δ)=sin θ−sin θ cos δ−sin δ cosθ.  (5)

For small rotation angle δ, the output angle issin α′_(i) ⁰(δ)≈−δ cos θ.  (6)

Compared with the original plane of grating G₀, the output angle is:sin α_(i) ⁰(δ)≈δ−δ cos θ=δ(1−cos θ).  (7)

As illustrated in FIG. 3B, the image light wave of G₀ is the input lightwaves to the grating G₁(x), that is:sin α_(c) ¹(δ)=sin α_(i) ⁰(δ)≈δ(1−cos θ).  (8)

Assuming that the two gratings G₁(x) and G₂(ξ) also have a non-zerocomponent only along the x axis, thensin α_(i) ¹(δ)=λG ₁+sin α_(c) ¹(δ)=sin α_(i) ¹(0)+δ(1−cos θ).  (9)

Hereinafter, the coordinates of the gratings G₁ and G₂ are denoted as(x,y,z) and (ξ,η,ζ), respectively. As illustrated in FIG. 3B, the imageray from G₁(x) “moves” leftward (i.e., in a negative direction) alongthe x axis of G₂(ξ) as a result of rotating G₀ by an angle δ, by adistanceΔξ=D(tan α_(i) ¹(δ)−tan α_(i) ¹(0)),  (10)where, D is the vertical distance between G₁(x) and G₂(ξ). Hence, a raythat emerges from point x on the grating G₁(x) for zero rotation havinga direction of α_(i) ¹(0) impinges on the grating G₂(ξ) at a point ξ,while for a rotation of δ the ray emerges from the same point x having adirection of α_(i) ¹(δ) and impinges on the grating G₂ at a point ξ−Δξ.For small rotating angle δ

$\begin{matrix}{{\tan{\alpha_{i}^{1}(\delta)}} - {\tan{\alpha_{i}^{1}(0)} \sim {\frac{\delta^{\prime}}{\cos^{2}\alpha_{i}^{1}}.{and}}}} & (11)\end{matrix}$ $\begin{matrix}{{{\sin{\alpha_{i}^{1}(\delta)}} - {\sin{\alpha_{i}^{1}(0)} \sim {\delta^{\prime} \cdot \cos}\alpha_{i}^{1}}},} & (12)\end{matrix}$where δ′=α_(i) ¹(δ)−α_(i) ¹(0). Therefore

$\begin{matrix}{{\tan{\alpha_{i}^{1}(\delta)}} - {\tan{\alpha_{i}^{1}(0)} \sim {\frac{{\sin{\alpha_{i}^{1}(\delta)}} - {\sin{\alpha_{i}^{1}(0)}}}{\cos^{3}\alpha_{i}^{1}}.}}} & (13)\end{matrix}$

Inserting Eqs. (9) and (13) into Eq. (10) yields

$\begin{matrix}{{\Delta\xi} = {{D\left( \frac{{\sin{\alpha_{i}^{1}(\delta)}} - {\sin{\alpha_{i}^{1}(0)}}}{\cos^{3}\alpha_{i}^{1}} \right)} = {\frac{D\left( {\delta\left( {1 - {\cos\theta}} \right)} \right)}{\cos^{3}\alpha_{i}^{1}}.}}} & (14)\end{matrix}$

Assuming that the light waves that are diffracted out of the gratingG₂(ξ) after a rotation of G₀ by an angle of δ, should be deviated by anangle of φ from the normal to the grating plane, then:α_(i) ²(δ)=φ,  (15)

As a result, the grating function at the point ξ−Δξ is:

$\begin{matrix}\begin{matrix}{{\lambda{G_{2}\left( {\xi - {\Delta\xi}} \right)}} = {{{- \sin}{\alpha_{c}^{2}\left( {\delta,\ {\xi - {\Delta\xi}}} \right)}} + {\sin{\alpha_{i}^{2}\left( {\delta,\ {\xi - {\Delta\xi}}} \right)}}}} \\{{= {{{- \sin}{\alpha_{i}^{1}(\delta)}} + {\sin(\varphi)}}},}\end{matrix} & (16)\end{matrix}$where, the −1 order is diffracted from grating G₂. Inserting Eq, (9)into Eq. (16) yields

$\begin{matrix}\begin{matrix}{{\lambda{G_{2}\left( {\xi - {\Delta\xi}} \right)}} = {{{- \sin}{\alpha_{i}^{1}(0)}} - {\delta\left( {1 - {\cos\theta}} \right)} + {\sin(\varphi)}}} \\{= {{{{\lambda G}_{1}(x)} - {\delta\left( {1 - {\cos\theta}} \right)} + {\sin(\varphi)}} \equiv {{- {{\lambda G}_{1}(x)}} + {\sigma \cdot \delta}}}}\end{matrix} & (17)\end{matrix}$where σ≡−(1−cos θ)+sin(φ)/δ is defined as the “angular amplificationfactor” of the DGE. σ is not dependent on x or ξ., and thus, σ is aconstant over the entire surfaces of the gratings. For δ=0 the inputlight waves to G₁(x) and the output light waves from G₂(ξ) are planewaves normal to the grating planes. As illustrated in FIG. 3A for δ=0the light ray is traced from the point x on G₁(x) to the point ξ onG₂(ξ). Therefore,λG ₂(ξ)=−λG ₁(x)=−sin α_(i) ¹(0).  (18)

Combining Eqs. (17) and (18) yields:λG ₂(ξ−Δξ)−λG ₂(ξ)=λG ₂(ξ−Δξ)+λG ₁(x)=σ·δ.  (19)

Dividing Eq. (19) by eq. (14) yields:

$\begin{matrix}{{\frac{{\lambda{G_{2}\left( {\xi - {\Delta\xi}} \right)}} - {\lambda{G_{2}(\xi)}}}{{- \Delta}\xi} = {\frac{\sigma \cdot \delta}{\frac{D\left( {\delta\left( {1 - \cos} \right)} \right)}{\cos^{3}\alpha_{i}^{1}}} = {{b \cdot \cos^{3}}\alpha_{i}^{1}}}},} & (20)\end{matrix}$where,

$b = \frac{\sigma}{D\left( {1 - {\cos\theta}} \right)}$is a constant. For small δ the following approximation may be written

$\begin{matrix}{{\frac{d\lambda{G_{2}(\xi)}}{d\xi} = {{{- b} \cdot \cos^{3}}\alpha_{i}^{1}}},} & (21)\end{matrix}$

Inserting Eq. (18) into Eq. (20) yields:

$\begin{matrix}{{\frac{d\;\sin\;\alpha_{i}^{1}}{\cos^{3}\alpha_{i}^{1}} = {{bd}\;\xi}},} & (22)\end{matrix}$

The solution of this equation is:

$\begin{matrix}{{{\tan\;{\alpha_{i}^{1}(x)}} = {{\tan{\alpha_{c}^{2}(\xi)}} = {b \cdot \xi}}},{or}} & (23) \\{\frac{\lambda{G_{2}(\xi)}}{\sqrt{1 - \left( {\lambda{G_{2}(\xi)}} \right)^{2}}} = {b \cdot {\xi.}}} & (24)\end{matrix}$

Where the boundary condition of λ G₂(ξ)=0 for ξ=0 is used, the solutionof this equation is:

$\begin{matrix}{{\lambda{G_{2}(\xi)}} = {\frac{b \cdot \xi}{\sqrt{1 + \left( {b \cdot \xi} \right)^{2}}}.}} & (25)\end{matrix}$

As illustrated in FIG. 3A, for δ=0x(ξ)=ξ+D tan α_(i) ¹(x)=ξ+D tan α_(c) ²(ξ).  (26)

Inserting Eq. (23) into Eq. (26) yields

$\begin{matrix}{{x(\xi)} = {{{\frac{1 + {b \cdot D}}{b} \cdot \tan}\;{\alpha_{i}^{1}(x)}} = {\frac{1 + {b \cdot D}}{b} \cdot {\frac{\lambda{G_{1}(x)}}{\sqrt{1 - \left( {\lambda{G_{1}(x)}} \right)^{2}}}.}}}} & (27)\end{matrix}$

The solution of this equation is

$\begin{matrix}{{{\lambda{G_{1}(x)}} = \frac{c \cdot x}{\sqrt{1 + \left( {c \cdot x} \right)^{2}}}},} & (34)\end{matrix}$where the constant c is defined as

${c \equiv \frac{b}{1 + {b \cdot D}}}.$

Since σ, the angular amplification factor of the DGE, is a constant overthe entire surfaces of the gratings, the deviation angle φ, for a givenrotation δ of the grating G₀, will be a constant for the entire DGE.Hence, a continuous change in rotation angle of the grating G₀ induces acontinuous angular steering of the output light wave from the gratingG₂(ξ), which is significantly amplified by the DGE in relation to theangular rotation of output wave from the grating G₀.

It is important to note that the solution given in Equations (25) and(28) is not the most accurate analytical one, but rather an approximatesolution, illustrating the capability of finding an easy and fastanalytical solution for the embodiment illustrated in FIGS. 3A and 3B.For most cases, however, this solution is accurate enough and enables asimple realization of a display system where for each pixel, a smallrotation of the grating G₀ can be significantly amplified by a DGE. Inaddition, the embodiment of FIGS. 3A and 3B can be used not only for apixelated display source, but also for other systems where a singlelight beam can be steered using a rotating grating and an amplifyingDGE.

In this context, a few alternatives for achieving the required angularsteering of an output beam using a single DGE were illustrated in FIGS.1-3. It is clear, however, that more than a single element is required,in order to achieve a display whose operation is based on the principleof manipulating light waves utilizing DGEs.

FIG. 4 illustrates an array of two different DGEs, which are locatedadjacent to each other, and can be controlled separately. Naturally,many more than two pixels are necessary to facilitate a display andusually a two dimensional array of pixels is required. FIG. 4 (and theFigures following same) is just an illustration as to how two differentDGEs may be utilized to form two pixels that are capable of emitting twodifferent light waves as part of a whole display. As shown, twodifferent DGEs, DGE¹ and DGE² are juxtaposed. (Hereinafter, for systemshaving a multiple number of DGEs, the superscript will denote theordinal number of a specific pixel). The structures of the two DGEs areidentical, i.e., the refractive index of the two substrates, which arelocated between the two DGEs respectively, can be controlled separatelyby applying two different electric currents on the substrates of thepixels. As seen in FIG. 4, two different refractive indices v¹≠v² areset for the two DGEs, and therefore, the two image light waves emergingfrom the DGEs are diffracted into two different directions, φ¹≠φ². For adynamic display, the controlling currents can be modified continuously,and therefore, the output directions of the light waves emerging fromthe pixels can be controlled accordingly. In this embodiment, theapproach using the electronically controllable refractive index isillustrated, however, other approaches such as those illustrated inFIGS. 1 and 3, or any other method that uses DGEs, may be utilized.

The beam steering illustrated in FIGS. 1-4 is performed only in the xaxis. A two-dimensional deviation for each pixel, however, can easily bematerialized by combining two different parallel DGEs for each pixel,whereby the scanning direction of each DGE is normal to that of theother. FIGS. 5A and 5B illustrate a system in which two pixels arepositioned adjacent to each other. Each pixel is composed of two DGEsoriented normal to each other. For each pixel, in addition to the DGED_(x) ^(i) having the gratings G₁ ^(i)(x), G₂ ^(i)(ξ) (i=1,2) in whichthe grating functions depend only on the x axis, a second DGE D_(y)^(i), having the gratings H₁ ^(i)(y), H₂(η) (i=1,2) in which the gratingfunctions depend only on the y axis, which is orthogonal to the x axis,is positioned on top of the DGE D_(x) ^(i). As illustrated in FIG. 5A,the light waves first pass through D_(x) ^(i) and are rotatedaccordingly around the y axis by an angle φ_(x) ^(i), which is set bycontrolling the refractive index v_(x) ^(i) of the first DGE D_(x) ^(i).The light waves then pass through the second DGE D_(y) ^(i), wherein therotation around the y axis is not influenced by the DGE. As illustratedin FIG. 5B, the rotation around the x axis is not influenced when thelight waves pass through the first DGE D_(x) ^(i). The light waves thenpass through the second DGE D_(y) ^(i) and are rotated accordinglyaround the x axis by an angle φ_(y) ^(i), which is set by controllingthe refractive index v_(y) ^(i) of the second DGE D_(y) ^(i). Since therefractive indices of the two orthogonal DGEs, belonging to the samepixel can be controlled separately, the exact two dimensional deviationof the output angle φ_(x) ^(i), φ_(y) ^(i) can be set by the controlsystem.

In the system illustrated in FIGS. 5A and 5B, the two verticallyadjacent gratings in each pixel, G₂ ^(i)(ξ) and H₁ ^(i)(γ), arefabricated separately. There are systems however, where it is simpler tocombine these two grating together to form a unified grating GH^(i)(ξ,y)having the grating function which is the combination of these twogratings, namely:{right arrow over (GH)} ^(i)(ξ,y)={right arrow over (G ₂^(i))}(ξ)+{right arrow over (H ₁ ^(i))}(y).  (29)

There are some opposing considerations for the manner in which thestructure of a two DGEs pixel can be fabricated. On the one hand, fromthe point of view of a simple assembly process, it is preferable tounify the two adjacent gratings as described above. On the other hand,it is usually much simpler to separately fabricate a one dimensionalgrating, such as G₂ ^(i)(ξ) or H₁ ^(i)(y) than it is to fabricate thetwo-dimensional grating GH^(i)(ξ,y), which can sometimes have acomplicated grating function. Therefore, the specific fabrication methodfor each system can be determined according to the detailed parametersof each system.

Another approach for achieving the required two-dimensional scanning,which differs from that described in FIGS. 5A and 5B, is to utilize asingle DGE instead of two adjacent orthogonal DGEs, wherein each gratinghas a two dimensional grating function depending on the x, as well asthe y coordinates. The system should contain a dynamic control unit,which will be capable of setting the deviation angle around the twoaxes. One possibility is to modify the optical system illustrated inFIG. 2 by using a substrate having a dynamic birefringent material inwhich the refractive index can be controlled separately along twoorthogonal axes. Another method is to modify the system illustrated inFIG. 3 by using a grating G₀, which can be rotated around the x, as wellas they axes.

A different method, based on the optical system shown in FIG. 1, isillustrated in FIGS. 6A and 6B. The reciprocal grating function of thesecond grating G₂(ξ,η,ζ) is defined as:

$\begin{matrix}{{{\overset{\rightarrow}{G_{2}}\left( {\xi,\eta,\zeta} \right)} = \left( {\frac{1}{d_{\xi}},\frac{1}{d_{\eta}},\frac{1}{d_{\eta}}} \right)},} & (30)\end{matrix}$where, (d_(ξ), d_(η), d_(ζ)) are the distances between two adjacentgrating lines at a given point (ξ,η,ζ) along the ({right arrow over(ι)},{right arrow over (η)},{right arrow over (ζ)}) axes, respectively.Since the grating plane is normal to the {right arrow over (ζ)} axis,the grating function can be written as:

$\begin{matrix}{{\overset{\rightarrow}{G_{2}}\left( {\xi,\eta} \right)} = {\left( {\frac{1}{d_{\xi}},\frac{1}{d_{\eta}}} \right).}} & (31)\end{matrix}$

Assuming that the grating function of the grating G₂ has a radialsymmetry, it can be written that G₂(ξ,η)=G₂(ρ), wherein ρ√√{square rootover (ξ²+η²)} is the radial distance between a given point (ξ,η) and thecenter of the grating and wherein d_(ρ), the radial distance between twoadjacent grating lines at a given point (ξ,η) is given by the equation

$\frac{1}{d_{\rho}} = {\sqrt{\left( \frac{1}{d_{\xi}} \right)^{2} + \left( \frac{1}{d_{\eta}} \right)^{2}}.}$

A grating G₂ having the grating function of the form:

$\begin{matrix}{{{\overset{\rightarrow}{G_{2}}(p)} = {{- \left( \frac{\rho}{\Lambda} \right)}\overset{\rightarrow}{\rho}}},} & (32)\end{matrix}$is chosen,wherein, Λ is a constant, the minus sign denotes that the −1 order ofthe grating G₂ is utilized and {right arrow over (ρ)} is the radial unitvector. The grating function is linearly monotonic increasing as afunction of the radius ρ. In that case, the various components of thegratings G₂ are:

$\begin{matrix}{{{G_{2\rho}(\rho)} = {- \left( \frac{\rho}{\Lambda} \right)}}{{G_{2\xi}(\xi)} = {{{- \left( \frac{\xi}{\Lambda} \right)}{G_{2\eta}(\eta)}} = {- {\left( \frac{\eta}{\Lambda} \right).}}}}} & (33)\end{matrix}$

The diffraction equation from a grating is given by:{right arrow over (V)} _(L)=λ{right arrow over (G ₂)}+{right arrow over(V)} _(c),  (34)wherein, {right arrow over (V_(i))} and {right arrow over (V_(c))} arethe vectors of the image and the reconstructing light waves,respectively. The components of these vectors can be written as:k _(i) =λG _(2ρ) +k _(c).l _(i) =λG _(2ξ) +l _(c)m _(i) =λG _(2η) +m _(c),  (35)wherein, λ is the wavelength of the diffracted light waves, k, l and mare the components of the light waves vectors (or the direction cosines)along the ρ, ξ and η axes, respectively.

As illustrated in FIG. 6A, without loss of generality, it is assumedthat image light wave which is diffracted from the grating G₂ is a planewave normal to the grating's plane, that is to say:{right arrow over (V)} _(i) =k _(i) =l _(i) =m _(i)=0.  (36)

As a result, the direction cosines of the reconstructing wave {rightarrow over (V)}_(c) should be:

$\begin{matrix}{{k_{c} = {{{- \lambda}G_{2\rho}} = \left( \frac{\lambda\rho}{\Lambda} \right)}}{l_{c} = {{{- \lambda}G_{2\xi}} = \left( \frac{\lambda\xi}{\Lambda} \right)}}{m_{c} = {{{- \lambda}G_{2\eta}} = {\left( \frac{\lambda\eta}{\Lambda} \right).}}}} & (37)\end{matrix}$

As illustrated in FIG. 6B, the grating is now translated by Δρ, whereinΔρ=√{square root over (Δξ²+Δη²)}. Therefore, a point (ξ,η) at thesurface of the second grating G₂ is now positioned compared to the firstgrating G₁, at the same location where the point (ξ+Δξ, η+Δη) waspositioned before the translation. As a result, the point (ξ,η) at thesurface of the second grating G₂, is illuminated after the translationby a readout ray having the direction cosines of:

$\begin{matrix}{{{k_{c}^{\Delta\rho} = {\left( \frac{\lambda\left( {\rho + {\Delta\;\rho}} \right)}{\Lambda} \right) = \left( {\frac{\lambda\rho}{\Lambda} + \frac{\lambda\Delta\rho}{\Lambda}} \right)}}{k_{c}^{\Delta\xi} = {\left( \frac{\lambda\left( {\xi + {\Delta\xi}} \right)}{\Lambda} \right) = \left( {\frac{\lambda\xi}{\Lambda} + \frac{\lambda\Delta\xi}{\Lambda}} \right)}}{k_{c}^{\Delta\eta} = {\left( \frac{\lambda\left( {\eta + {\Delta\eta}} \right)}{\Lambda} \right) = \left( {\frac{\lambda\eta}{\Lambda} + \frac{\lambda\Delta\eta}{\Lambda}} \right)}}}.} & (38)\end{matrix}$

Inserting Eqs. (33) and (38) into Eq. (34) yields:

$\begin{matrix}{{{k_{i}^{\Delta\rho} = {{{\lambda G_{2\rho}} + k_{c}^{\Delta\rho}} = {{{- \frac{\lambda\rho}{\Lambda}} + \left( {\frac{\lambda\rho}{\Lambda} + \frac{\lambda\Delta\rho}{\Lambda}} \right)} = \frac{\lambda\Delta\rho}{\Lambda}}}}{l_{i}^{\Delta\xi} = {{{\lambda G_{2\xi}} + l_{c}^{\Delta\xi}} = {{{- \frac{\lambda\xi}{\Lambda}} + \left( {\frac{\lambda\xi}{\Lambda} + \frac{\lambda\Delta\xi}{\Lambda}} \right)} = \frac{\lambda\Delta\xi}{\Lambda}}}}}{m_{i}^{\Delta\;\eta} = {{{\lambda G_{2\eta}} + m_{c}^{\Delta\eta}} = {{{- \frac{\lambda\eta}{\Lambda}} + \left( {\frac{\lambda\eta}{\Lambda} + \frac{\lambda\Delta\eta}{\Lambda}} \right)} = {\frac{\lambda\Delta\eta}{\Lambda}.}}}}} & (39)\end{matrix}$

The direction of the image ray {right arrow over (V)}_(i) ^(Δρ)(ξ,η) isinvariant to the point (ξ,η) at the surface of the second grating G₂,meaning that the entire light wave impinging on the surface of thesecond grating, is diffracted to the same direction, and hence, theimage wave is a pure plane wave having the direction cosines of Eq.(39).

In order to calculate the requested grating function {right arrow over(G₁)}(r) of the first grating, a ray from a given point ρ on the secondgrating to the respective point r(φ on the first grating can be traced,wherein the two gratings are positioned at the default zero position,i.e., wherein Δρ=0.

As illustrated in FIG. 7, the lateral distance along the radial axisbetween ρ and r(ρ) is given by:r(ρ)=ρ+D·tan(β),  (40)wherein, D is the distance between the two gratings and the directioncosine of the ray which is traced from r(ρ) to ρ is:k _(c)(ρ)=k _(i)(r)=sin(β).  (41)

Inserting Eq. (37) into (41) yields

$\begin{matrix}{{{\sin(\beta)} = \left( \frac{\lambda\rho}{\Lambda} \right)}.} & (42)\end{matrix}$

Inserting Eq. (42) into (40) yields

$\begin{matrix}{{r(\rho)} = {\frac{\Lambda{\sin(\beta)}}{\lambda} + {d \cdot {{\tan(\beta)}.}}}} & (43)\end{matrix}$

It is assumed that without loss of generality, the readout light wavewhich illuminates the first grating G₁ is a plane wave normal to thegrating's plane, namely, that k_(c)(r)=0.

As a result, the grating function {right arrow over (G₁)}(r) of thefirst grating is:

$\begin{matrix}{{{\overset{\rightarrow}{G_{1}}(r)} = {{\frac{k_{i}(r)}{\lambda}\overset{\rightarrow}{r}} = {\frac{\sin(\beta)}{\lambda}\overset{\rightarrow}{r}}}},} & (44)\end{matrix}$wherein {right arrow over (r)} is the radial unit vector. Therefore, theabsolute value of the grating {right arrow over (G₁)}(r) is:

$\begin{matrix}{{{G_{1}(r)} = {\frac{k_{i}(r)}{\lambda} = \frac{\sin(\beta)}{\lambda}}},{or}} & (45)\end{matrix}$ $\begin{matrix}{{\sin(\beta)} = {\lambda{{G_{1}(r)}.}}} & (46)\end{matrix}$

Inserting Eq. (46) into (43) yields

$\begin{matrix}{{{r(\rho)} = {{\Lambda{G_{1}(r)}} + \frac{d \cdot {G_{1}(r)}}{\sqrt{1 - {\lambda^{2}{G_{1}^{2}(r)}}}}}}.} & (47)\end{matrix}$

This is a simple monotonic increasing function, and therefore, theinverse function G₁(r) can easily be found. The direction cosine mustfulfil the condition:

$\begin{matrix}{{{k_{c}(\rho)} = {\frac{\lambda\rho}{\Lambda} = {{\sin(\beta)} \leq 1}}}.} & (48)\end{matrix}$

Therefore, the maximal radial distance from the center of the grating G₂is:

$\begin{matrix}{{\rho_{\max} \leq \frac{\Lambda}{\lambda}}.} & (49)\end{matrix}$

Utilizing Eq. (39) yields:

$\begin{matrix}{{\frac{\lambda}{\Lambda} = {\frac{k_{i}^{\Delta\rho}}{\Delta\rho} \leq \frac{1}{\rho_{\max}}}}.} & (50)\end{matrix}$

As a result, the maximal angular deviation that can be obtained from thedouble grating assembly illustrated in FIGS. 6A, 6B and 7 is

$\begin{matrix}{k_{i}^{\Delta\rho} \leq {\frac{\Delta\rho}{\rho_{\max}}.}} & (51)\end{matrix}$

In all of the systems illustrated in FIGS. 1-6, it was assumed that thedisplays are illuminated by monochromatic light waves having a singlewavelength λ. In almost all of the illustrated display systems, however,the display should have the capability of projecting full color images.One approach for achieving a colorful display, especially forapplications where the picture element size is comparatively large, isto utilize a Fresnel element instead of diffraction gratings,cylindrical for the embodiments of FIGS. 1-5, and circular elements forthe embodiment of FIGS. 6A and 6B, as the basic elements for the pictureelements. In that case, it is possible to design the Fresnel elementssuch that they will obey Eqs. (1)-(51), and in addition, theirsensitivity to the reconstructing wavelength will be much lower and awhite light can be used to illuminate them. For diffractive gratings,however, the sensitivity to the reconstructing wavelength is very high,and each picture element has to be reconstructed with a monochromaticlight. Therefore, at least three different images, having threedifferent colors, respectively, should be multiplexed together to createthe required colorful image. There are two main methods to facilitatethe required color multiplexing. One method is the time sequential colorimaging, in which the color images are generated by sequentially layingdown three basic colors of red, green, and blue (RGB) light in a singleimage frame, which typically lasts 1/f of a second, where f is thefrequency of the system, usually 50 or 60 hertz. This means that theperiod time frame is divided into three equal sub-periods, wherein ineach one, only one color is illuminating the display. It is possible toutilize this method for the present invention by fabricating each one ofthe grating in the DGE as a multiplexed grating which is composed ofthree overlapping gratings, each one being sensitive to one of the threebasic colors and non-sensitive to the other two colors. The main problemof using this approach to illuminate DGE is that it is usually difficultto achieve high diffraction efficiencies for a multiple grating. As aconsequence thereof, there is a risk of a “cross-talk” of the lightwaves between the three overlapped gratings (that is, a light wave willbe diffracted by the “wrong” grating), resulting in the color qualityand the contrast of the image being degraded.

An alternative method for achieving a color display is to utilize thecolor-filter approach. Each pixel in the display is divided into threesubpixels wherein the color-filter process adds three basic RGB colordyes or pigments to each subpixel so that by mixing the three primarycolors, almost any color can be generated. The main disadvantage of thismethod is that the display is illuminated by a white light wave, or by amixing of three different light waves having different RGB colors,respectively. As a result, all of the subpixels are illuminated by thethree different light waves, where only one of them, having theappropriate color, passes through the color filter, while the other twolight waves having the “wrong” color, are absorbed. Therefore, thetransmittance efficiency of color-filter display is reduced by a factorof at least three.

FIGS. 8A-8C illustrate an alternative method for illuminating a displaysource using an array of DGEs, to achieve a high efficient system. Asillustrated in FIG. 8A, an input light wave W_(rgb) ^(i), which is a mixof three plane light waves, W_(r) ^(i), W₉ ^(i) and W_(b) ^(i), havingthe colors RGB, respectively, impinges on a DGE D_(rgb) normal to thegrating's plane. The first grating C_(rgb1)(x), having a lateraldimension of a_(x), is a multiplexed grating of three different gratingsC_(r1)(x), C_(g1)(x) and C_(b1)(x), each of which is sensitive to theRGB colors, respectively, but not sensitive to the other two colors. Thesecond grating is composed of three adjacent separated gratings,C_(r2)(ξ), C_(g2)(ξ) and C_(b2)(ξ), each one having a lateral dimensionof a_(x)/3, which are sensitive to the RGB colors, respectively. The RGBlight waves (dotted, dashed and solid line, respectively) are diffractedfrom the first grating to the second grating and the output light waveswhich emerge from the second grating are also plane waves normal to thegrating's plane, therefore−λ_(c) G _(c2)(ξ)=λ_(c) G _(c1)(x)=sin α_(i) ¹(x)=sin α_(c)²(ξ),c=r,g,b  (52)wherein, each light ray is traced from the point x on G₁ to the point ξon G₂. Therefore,ξ(x)=x+D tan α_(c) ²(ξ).  (53)

Each one of the three sub-gratings of the second grating C_(rgb2)(ξ) canbe very efficient to its respective color. Indeed, since the firstgrating C_(rgb1)(x) is multiplexed of three different gratings, itcannot be 100% efficient. The “cross-talk” between the three gratingscan, however, be avoided by placing a color filter having sub-filtersF^(r), F^(g) and F^(b) in front of the three gratings C_(r2)(ξ),C_(g2)(ξ) and C_(b2)(ξ), respectively. Since each one of thesub-gratings is now illuminated by a light wave having mostly the“right” color, and only a small percentage thereof is from the “wrong”color, the energy loss due to the filters will be minimal but the“cross-talk” will actually be prevented.

As illustrated in FIG. 8B, the three color separated output light wavesfrom D_(rgb) can be utilize to illuminate three subpixels, each onehaving its respective DGE D^(c) (the super script c=r,g,b denotes thecolor of the respective DGEs). The directions of the three output lightwaves W_(c) ^(o) from the subpixels are set by controlling therefractive indices of the substrates which are respectively locatedinside the three DGEs. As discussed hereinabove with regard to FIGS. 5Aand 5B, here too the vertically adjacent gratings in each subpixel,C_(c2)(ξ) and G₁ ^(c)(x), can be fabricated separately. There aresystems, however, where it is simpler to combine these two gratingtogether into a unified grating having the grating function which is thecombination of these two gratings. As previously stated, the specificfabricated method for each system can be determined according to thedetailed parameters of each system.

As shown in FIGS. 8A and 8B, there is a shift of D·tan α_(b)(0) betweenthe two gratings of D_(rgb) wherein, D is the vertical distance betweenthe gratings and α_(b)(0) is the direction of the blue ray that connectthe points x=0 with ξ=0. The overall lateral aperture of the twogratings is, however, equal to a_(x).

FIG. 8C illustrates two adjacent color-filtered pixels which areilluminated utilizing two respectively contiguous DGEs. As previously,the output light waves W_(c) ^(oi) (i=1,2; c=r,g,b) from the sixsubpixels are set by controlling the respective refractive index insidethe DGE of each subpixels. For a large number n of pixels, the overallaperture of the display will be n·a_(x), and the shift between the planeof the first grating and that of the second gratings will be negligible.As a result, the fill-factor of the display is substantially 1.

In the systems illustrated in FIGS. 8B and 8C, the RGB illuminationmodule based on a DGE is utilized to back illuminate a display, whereinthe pixels are designed according to the method illustrated in FIG. 2.Eventually, this illumination method can also be utilize for displayswherein the pixels are designed according the alternative methodsillustrated in FIGS. 1, 3 and 6, respectively. Moreover, thisillumination method can also be utilized not only for displays whereinthe pixels are composed of DGEs, but also for other conventionaldisplays. FIG. 9A illustrates a method wherein a DGE-based module isutilized to back illuminate a

Liquid Crystal Display (LCD), wherein usually a backlight module shouldbe added to the back side of the display. As shown, an illuminationelement D_(rgb) is located at the back surface of a single pixel 20,which was divided into three subpixels 22, 24, and 26, respectively, anddesignated for the blue, green and red colors, respectively. Thesplitting of the three basic colors, W_(r) ^(i), W_(g) ^(i) and W_(b)^(i), from the input light wave W_(rgb) ^(i), is performed in a similarmanner to that described in relation to FIG. 8A. The output light waves,W_(r) ^(o), W_(g) ^(o) and W_(b) ^(o), diverge from the subpixels by adiffuser 28 which is usually a part of the LCD. Typically, the LCD isnot illuminated by a combination of three monochromatic light waves, asutilized in FIG. 8A, but rather by a light having combination of threechromatic bands, or even by white light waves. As a result, theefficiencies of the D_(rgb) gratings will not be optimal, and totaloutput efficiency will be degraded, even though the efficiency that maybe achieved by a DGE-based illumination module, can be significantlyhigher than the maximum of 33%, which can be achieved with the existingillumination modules.

FIG. 9B illustrates a method wherein a DGE-based module is utilized tofront illuminate a Liquid Crystal on Silicon (LCOS) display. Similar toLCD panels, LCOS panels contain two-dimensional array of cells filledwith liquid crystals that twist and align in response to differentvoltages. With LCOS, the liquid crystal elements are grafted directlyonto a reflective silicon chip. According to the liquid crystals thattwist following reflection of the mirrored surface below, thepolarization of the light is either changed or unchanged, creatingbright or dark pixels, respectively. As illustrated, the front surfaceof the pixel 30, which is divided into three subpixels 32, 34 and 36, isilluminated by the input light wave, W_(rgb) ^(i), in a similar mannerto the illumination scheme of the back surface of an LCD, as shown inFIG. 9A. The main difference is that in this case, the output lightwaves, W_(r) ^(o), W_(g) ^(o) and W_(b) ^(o), do not pass through thepixels, but are rather reflected back from the front surfaces of thepixels, in an opposite direction to their original direction.

An issue which should be taken onto account when designing a frontillumination of an LCOS utilizing DGEs is the diffraction efficienciesof the second gratings C_(c2)(ξ) While the polarization of light wavesthat are diffracted by the gratings of the DGE into the illuminationmodule of an LCD remains the same, the polarization of the light waveswhich are reflected from “bright” pixels of a LCOS, is rotated by 90°.As a result, the efficiencies of the two orthogonal polarizationspassing through the gratings should be taken into account. There are twopossible alternatives for efficiently using the scheme illustrated inFIG. 9B, namely, the gratings should either be very efficient, oralternatively, totally inefficient to the orthogonal polarization.

FIG. 10A illustrates a system wherein the gratings are very efficientfor the two orthogonal polarizations. As shown, the reflected waves fromthe two adjacent pixels 40 and 42, are diffracted back, and return tothe original locations where they entered the system, substantiallynormal to the gratings plane, where the two output light waves, W_(rgb1)^(o) and W_(rgb2) ^(o) from the two pixels 40 and 42, are separated fromeach other.

FIG. 10B illustrates a different scenario in which the gratings arehighly efficient only for the incoming polarization, while theefficiency for the orthogonal reflected polarization is negligible. Inthis case, the reflected output light waves, W_(rgb1) ^(o) and W_(rgb2)^(o) from the two pixels 40 and 42, pass without any significantdiffraction through the various gratings. The position of the outputlight waves is now shifted relative to the original entrance location,but the two light waves remain laterally separated. It should be notedthat in this configuration the light waves, which are reflected from“dark” pixels, retain their original polarization, and hence, will againbe diffracted by the gratings as shown in FIG. 10B. These light waveswith the “undesired” polarization, however, will eventually be blockedby a polarizer at the exit surface of the illumination module, and hencetheir exact locations have no importance.

The situation, however, becomes undesirable for systems wherein thegratings are partially sensitive to the polarization of the reflectedlight waves. As illustrated in FIG. 10C, a part of the light waveW_(rgb2) ^(o), which is reflected from pixel 42, is again diffracted bythe gratings, wherein a part of the other output light wave W_(rgb1)^(o), which is reflected from pixel 40, passes through the gratings. Thetwo reflected output light waves now at least partially overlap, and asa result the contrast of the image will be severely deteriorated.

The methods illustrated in FIGS. 1-9 for providing display systems inwhich not only the intensity of the emitted light wave from each pixel,but also the direction of the beam can be controlled, are usable toenable numerous types of displays that can be facilitated by utilizingthe existing technologies.

FIG. 11A illustrates the simplest implementation of the DGE-baseddisplay. Instead of continuous scanning of the output light wave light,each pixel has only two states. As shown in the Figure, the pixel P₁ isin the “off” state, where the controlled refractive index is set tov_(d), and deviates the output light wave by an angle P₂. The deviatedlight wave is then obstructed by a blocker 44, and is thereforeprevented from propagating to the exit pupil of the system. The pixel P₂is set to the “on” state, where the refractive index v_(b) causes theoutput light wave to be emitted normal to the pixel plane, and hence, toabort the blocker 44 and continue without interruption to the exit pupil45 of the system. The grayscale of the pixel can be determined bycontrolling the ratio of on-time to off-time, for each frame and pixel,respectively. The blocker illustrated in FIG. 11A is merely an exampleof how to block the deviated light during the off-time. Other methodsare possible, including designing the optical system such that thedeviated light waves will miss the output aperture of the system, oralternatively, placing the blocker in another location. The location towhich the undesired light waves are diverted is usually called a heatsink or a light dump.

The output light waves illustrated in FIG. 11A are plane waves. In mostof the displays, however, it is required that the emitted light wavesfill the output aperture (or the required viewing angles for flatscreens), and therefore, as illustrated in FIG. 11B, the output lightwaves should be diverged into a pre-defined solid angle Δθ. Thedivergence of the light waves is partially achieved by some of the basicoptical parameters of the system, such as the pre-divergence of theinput light waves, the chromatic bandwidth of quasi-monochromatic lightsources and the diffraction from the finite size of the pixel. The exactrequired divergence of the light beams may be obtained by adding anangular-selective diffuser 46 at the exit surface of the pixel, oralternatively, at the input surface. In any case, care should be takenduring the optical design of the display that the entire diverged lightwaves in the “off” state will go to the heat sink, and not pass theoutput aperture of the system.

The bi-state operation principle of the displays illustrated in FIGS.11A and 11B is similar to that of a Digital Light Processing (DLP) inwhich each pixel is composed of a tiny mirror that can rapidly berepositioned to reflect light either through the output aperture of thesystem, or onto a heat sink. The main advantage of the present inventionover the DLP is that the main principle is based on a transmission oflight through the display, as opposed to the DLP where the light isreflected from the display. As a result, the optical design here will bemuch simpler and the overall volume may be much smaller than that of aDLP.

In order to understand the potential of the new display technology,wherein for each pixel not only the intensity of light wave which isemitted is controlled, but also the direction of the emitted wave, it isimportant to understand the principle of the displays. FIG. 12illustrates a prior-art, conventional flat display 50, wherein for anygiven frame time each pixel emits a diverging light wave having anexpanding angle of φ_(FOV). This angle usually denotes the actual fieldof view (FOV) of the display and for a high-quality flat screen it canreach up to 2π steradian solid angle. The main outcome of the principleof operation is that for any given time frame, each pixel emits the sameinformation to all directions. As a result, the same light from pixel 52impinges on both of the viewer's eyes 54 (neglecting small variations ofintensity). Consequently, the viewer sees the same image from anyrelevant viewpoint, and the image is considered two-dimensional.

A totally different display principle in which the direction of thelight emitted from each pixel, can be controlled utilizing DGE basedpixels, is illustrated in FIG. 13. As shown, during two different timest₁ and t₂ in the same frame time, namely, for t₁ and t₂ fulfilling thecondition of 0<t₁<t₂<T_(i), wherein T_(f) is the duration of the frametime of the display, two different output light waves W_(o)(t₁) andW_(o)(t₂) are emitted from the display 56. Indeed, the two light wavesare emitted on two different occasions however, since they are includedinside the same frame time, they will actually appear simultaneously tothe viewer's eyes. The reason for this is the persistence of vision,wherein multiple discrete images blend into a single image in the humanmind. As a result, two different rays 59 a and 59 b originating from thetwo images W_(o)(t₁) and W₀(t₂), are emitted during the same frame timefrom pixel 58 and impinge on the viewer's eyes, 60 a and 60 b,respectively. Consequently, the viewer can see the two different imagesfrom two viewpoints and can conceive the image as a stereoscopic one.

A three-dimensional image, having many more than two differentviewpoints, can actually be obtained by the DGE scanning technology. Atthe first stage, a display system having a three-dimensional effect onlyin the horizontal axis x is considered. It is assumed that it isnecessary for any emitted image from the display, at any given timeframe, should consist of n different sub-images in n viewpoints v_(j)(j=1 . . . n) along the x axis. To achieve this, the emitted image waveW_(o) from each pixel should be scanned along the x axis during the timeframe to cover the entire solid angle of the FOV, namely, to eachrequired viewpoint v_(j) (assuming that they are uniformly located overthe FOV), a viewing angle φ_(j) is designated whereby the scanned waveis deviated at time t_(j).

FIG. 14 illustrates a pixel wherein the refractive index v(t) betweenthe two gratings is modified as a function of time. As shown, at twodifferent times, t₁ and t₂, in the same time frame, the image wave isdeviated to two different angles φ₁ and φ₂, respectively. For eachviewpoint, v_(j) a maximal time slot of Δτ=T_(f)/n is dedicated, wherebythe output light wave is deviated to this specific viewpoint. Onepossible method for controlling the intensity of the output light waveat each viewpoint is by placing a conventional LCD in front of theexternal gratings G₂(ξ). With the minimal response rate achievable inthe existing LCD technology, however, only a very small number ofdifferent viewpoints can be achieved. It is therefore preferable to usean alternative method by controlling the angular scanning velocity ofthe output light wave W_(o), namely, for each viewpoint v_(j) and eachpixel at any given time frame, an actual time slot Δτ_(j) is dedicatedwherein, 0≤Δτ_(j)≤Δτ. The grayscale of the light wave is determined bythe time A_(T), wherein for a totally dark pixel Δτ_(j)=0 and for atotally bright pixel Δτ_(j)=Δτ. Only for a bright pixel over the entireFOV is the condition Σ_(j=1) ^(n) Δτ_(j)=T_(f) fulfilled. For most ofthe cases Σ_(j=1) ^(n) Δτ_(j)<T_(f), and hence, for any time t thatfulfils Σ_(j=1) ^(n) Δτ_(j)<t<T_(f), the output light wave is deviatedinto the heat sink.

As illustrated in FIG. 15, which shows two consecutive output lightwaves W_(o)(t_(j)) (solid lines) and W_(o)(t_(J+1)) (dashed lines), inorder for the scanned wave to cover the entire FOV without gaps in theimage, the angular divergence of the wave should be Δφ=φ_(FOV)/n.Practically, it would be much simpler to deviate the output light waveby a continuous scanning, rather than by a discrete number ofdeviations, and therefore, the grayscale of the output light waveW_(o)(t_(j)) will be determined by the angular scanning velocity

${\omega_{i} = \frac{\Delta\varphi}{\Delta\tau_{j}}}.$The time t_(j) that a specific pixel will emit the output light wave toa given direction φ_(j), depends on the brightness of the previousangles and the actual velocity of the angular scanning prior to thattime. Specifically,t _(j)=Σ_(i=1) ^(j-1)Δτ_(i).  (54)

As a result, since the scanning angular velocity depends on the overallbrightness of the specific pixel t_(j), it is therefore different foreach pixel, and consequently, the light waves from the various pixelswill arrive into the viewpoint v_(j) at different times. All of thesetimes, however, are contained in the same time frame, namely,0≤t_(j)≤T_(f) for all the pixels in the display. Therefore, because ofthe persistence of vision, the light waves from all the pixels will beintegrated into the viewer's eye, thereby creating a single image.

An important issue to take into account is the luminance L_(v) (i.e.,emitted energy per unit time per unit solid angle per unit projectedsource area) of the projected image. Seemingly, since an output lightwave from a bright point is emitted only for a time of Δτ, which islower by a factor of n than the emitting time T_(f) of a conventionaldisplay, and both times are smaller than the integration time of theeye, the brightness to the viewer's eye will be lower by the same factorn, accordingly. This brightness decrease may be compensated by the lowerangular divergence of the emitted light wave. As explained above, theangular dispersion of the output light wave in the display illustratedin FIGS. 14 and 15 is Δφ=φ_(FOV)/n, while for a conventional display itis φ_(FOV), namely,

$\begin{matrix}{{\varphi^{dge} = \frac{\varphi^{con}}{n}},} & (55)\end{matrix}$wherein, the superscript dge and con denote the parameters of DGE-basedand conventional displays, respectively. It is assumed that the luminousemittance M_(v) (i.e., emitted energy per unit time per unit projectedsource area) of the light waves is the same for the two displays, hence,M _(v) ^(dge) =M _(v) ^(con).  (56)

Combining Eqs. (55) and (56) yields:

$\begin{matrix}{L_{v}^{dge} = {\frac{M_{v}^{dge}}{\varphi^{dge}} = {\frac{n \cdot M_{v}^{con}}{\varphi^{con}} = {n \cdot {L_{v}^{dge}.}}}}} & (57)\end{matrix}$

This means that the instantaneous luminance of the DGE-based display ishigher by a factor of n than that of a conventional display whichcompensates the shorter time illumination of the former display. Asdescribed above, part of the required divergence of the output lightwave φ_(p) is achieved by the basic optical parameters of the system. Aspreviously stated, the exact required divergence of the light beams canbe obtained by adding an angular-selective diffuser 62 (FIG. 15) at theexit surface of the pixel, or alternatively, at the input surface, themain difference here being that a different divergence is required alongthe x and the y axes. While the required divergence in the x axis is Δφ,for the y axis the beam should cover the entire FOV and the requireddivergence angle is φ_(FOV). To achieve this requirement, anon-symmetrical angular-selective diffuser may be used, wherein thediffusion angle along the x axis is much narrower than that along the yaxis. Assuming that the FOV_(x) along the x axis is different thanFOV_(y) along they axis, yields the following required diffuser'sangles:

$\begin{matrix}{{\varphi_{difx} = {\frac{\varphi_{FOVx}}{n} - \varphi_{p}}};{\varphi_{dify} = {\varphi_{FOVy} - {\varphi_{p}.}}}} & (58)\end{matrix}$

So far, it has been assumed that the three-dimensional effect isrequired only along the x axis, when actually, depending on the scanningcapabilities of the system, it is possible to achieve this effect alsoalong the y axis. Assuming that instead of a single viewpoint v_(j) onthe viewing angle φ_(j), a vertical row of m different viewpoints arerequired, namely, the image is composed of a total number of n*mdifferent viewpoints v_(ji), each having two orthogonal viewing angles(φ_(xj), φ_(yi)). The two-dimensional scanning can be performed usingthe methods described above in relation to FIGS. 5 and 6. The variousparameters of the system will now be:

$\begin{matrix}{{{\Delta\tau} = \frac{T_{f}}{n \cdot m}};{{\Delta\varphi}_{x} = \frac{\varphi_{FOVx}}{n}};{{\Delta\varphi}_{y} = {\frac{\varphi_{FOVy}}{m}.}}} & (59)\end{matrix}$

For each pixel and each viewing angle v_(ji) at any frame time, anactual time slot Δτ_(ji) is dedicated according to required brightness.Assuming that the scanning is performed by covering horizontal rows oneby one, the emitting time t_(ji) for each viewpoint v_(ji) is:t _(ji)=Σ_(k=1) ^(i-1)Σ_(l=1) ^(n)Δτ_(lk)+Σ_(l=1) ^(j-1)Δτ_(li),  (60)and the angular scanning velocity is

${\omega_{ji} = \frac{{\Delta\varphi}_{x}}{\Delta\tau_{ji}}}.$The images created in the embodiments illustrated in FIGS. 13-15 aremonochromatic images, which were produced utilizing a monochromaticlight wave, however, full-color images can easily be achieved utilizingcolor-sequential, or alternatively, color filter pixels, as describedhereinabove with regard to FIGS. 8-10.

FIGS. 13-15 illustrate systems wherein the display emits for any givenframe a discrete number of n different images into n differentviewpoints, arranged in one-dimensional or two-dimensional array. Itwill be advantageous, however, to exploit the technology of DGEs baseddisplay described in this invention, to obtain a full continuousthree-dimensional display, as is the case in holographic displays. Therecording and readout principles of a holographic display areillustrated in prior art FIGS. 16A and 16B, respectively. As shown inFIG. 16A, an interference pattern of two coherent light waves, theobject and the reference waves, is created on the holographic plate 63.Usually the object wave is scattered from a diffusive object, while thereference wave is a simple plane wave that can easily be reconstructed,wherein the two interfering waves have to originate at the same coherentsource, usually a laser beam. As illustrated, the reference ray 64interferes at a point 65 on the holographic plate 63 with threedifferent rays, 66, 67 and 68, emitted from three points 70, 72, and 74,respectively, on an object 75, namely, a multiple interference patternis created on point 65. In actual fact, the interference patterncontains many more than three different patterns, since the objectessentially emits a continuum of rays; only three rays are plotted herefor the sake of simplicity. A similar multiple interference pattern iscreated on point 78, where the reference ray 76 interferes with threedifferent rays, 80, 82 and 84, emitted from the same three points 70,72, and 74, respectively. Similar interference patterns are created as aresult of the interference between the various rays of the object andthe reference waves. The interferences patterns are usually recorded ona very high-resolution photographic emulsion, which is converted afterthe developing process into a complicated diffraction grating.

The reconstruction process of the holographic display is illustrated inFIG. 16B. A reconstructing wave, which is similar to the reference wave,illuminates the developed holographic plate 63. The reconstructing ray86, originating from the same direction as the reference ray 64 of FIG.16A, is diffracted from the interference pattern at point 65, to createthree image rays, 66″, 67″ and 68″, which are emitted from the plate atthe same directions that the rays 66, 67 and 68 (FIG. 16A) and impingeon the plate during the recording process. As a result, the viewer's eye90 sees these rays as they are the rays 66′, 67′ and 68′, which areemitted from the points 70, 72, and 74 on the object 75. Similarly, thereconstructing ray 89, originating from the same direction as thereference ray 76 (FIG. 16A), is diffracted from the interference patternat the point 78 to create three image rays, 80″, 82″ and 86″, and theviewer's eye 91 sees these rays as they are the rays 80′, 82′ and 86′,which are emitted from points 70, 72, and 74. The rays 66′, 67′ and 68′as well as rays 80′, 82′ and 86′, are not real, but rather virtual rays,and therefore, a virtual image 75′ is created at the location of theoriginal object 75. Similar diffraction of the reconstructing light waveoccurs at all the other points of the holographic plane 63, and theviewer sees a virtual three-dimensional image as it appears from a“window” located at the position of the holographic plate.

The main drawback of the photographically recorded holographic displayis that it can project only static images. In order to facilitate adynamic holographic display, a dynamic spatial light modulator (SLM) isrequired, which SLM can produce, in real time, the required complicateddiffraction pattern that will be able to diffract a simplereconstructing light wave into the desired dynamic three-dimensionalimage. Even with the most advanced currently existing projectiontechnologies, however, the highest achievable resolution is still lowerby an order of magnitude than the required resolution for the dynamicdisplay, which should be a sub-wavelength, i.e., a few thousandsline-pairs per millimeter.

An alternative approach for achieving a dynamic three-dimensionaldisplay by utilizing DGE based pixels, according to the presentinvention, is illustrated in FIG. 17. Instead of using a dynamicgrating, an array of fixed gratings producing the DGE-based display 93is utilized, wherein the dynamic image is produced by scanning theoutput light wave at each pixel in a manner that imitates thediffraction of the reconstructing light wave from a dynamic grating. Asillustrated, an input ray 95 that illuminates a pixel 97 is scanned at agiven time frame in various directions by the method similar to the onedescribed hereinabove with regard to FIGS. 14-15. The main difference isthat now the output light wave is scanned continuously to create thepattern of the required virtual image, as seen at the location of thepixel 97. As further shown, three different output rays 100, 101 and 102are emitted from pixel 97, and the viewer's eye 90 sees these rays asrays 100′, 101′ and 102′, which are emitted from the points 70, 72, and74 on the virtual image 75′. Similarly, the input ray 96 is scanned atpixel 98 to create three image rays, 105″, 106″ and 107″, and theviewer's eye 91 sees these rays as rays 80′, 82′ and 86′, which areemitted from the points 70, 72, and 74. It should be noted that here therays which create the virtual image 75′, are not emitted simultaneouslyas is the case in a holographic display, but rather sequentially. As aresult, a very fast scanning is required to create a detailed image.Naturally, the resolution of the projected virtual image is determinedby the achievable scanning velocity of the system. The above descriptionapplies only for a single time frame, wherein a single three-dimensionalvirtual image is formed. Obviously, on any time frame, a different imagemay be created, and therefore, the display can from a dynamic virtualimage which will be projected into the viewer's eyes. Full-color imagescan easily be constructed utilizing color-sequential, or alternatively,color filter pixels, as described hereinabove in relation to FIGS. 8-10.

Another appealing application that can be provided using the techniquedescribed herein is that of Fourier-transform displays. In almost all ofthe existing display sources, the image plane coincides with the displayplane, namely, the light waves emitted from the display create an imagewhich is located on the display plane, and each point of the image isrepresented by a single pixel located at a specific location on thedisplay. There are many applications however, such as bi-oculars,head-up displays (HUDs) and HMDs, wherein the required image should becollimated to infinity. In these systems, each point of the image isrepresented by a single plane wave impinging on the viewer's eye from aspecific viewing angle. Usually, in order to achieve the requiredcollimated image, the image from a conventional display source iscollimated to infinity utilizing an optical module. In other words, thecollimating optical module performs a Fourier transform of the realimage of the display and each diverging light wave from a single pixelis transformed into a plane wave which arrives from a specificdirection. For most of the applications, especially for those in whichwide FOV or high performance is required, the collimating optical modulebecomes large, heavy, cumbersome and expensive, significantlycomplicating the fabrication of the required system. This drawback isparticularly severe for optical systems such as HMDs, whereincompactness and light weight are crucial parameters. Another drawback ofthese systems is that the collimating module, even for the high-endapplications, usually imposes undesired aberrations into the collimatedwaves which degrade the optical quality of the image.

In order to a overcome these drawbacks, it would be preferable to have adisplay source that emits an assembly of plane waves instead of thediverging light waves which are emitted from the present displays. Oneapproach for achieving this goal is to utilize a high resolution SLM,wherein the light waves which are emitted from the display plane aremodulated according to the Fourier-transform of the required image. Thiscan be achieved if the transparency of the SLM itself will be modulatedas the Fourier transform of the real image and by illuminating the SLMplane with a simple plane wave such that the output light wave will bemodulated accordingly. The main problem with this approach is that toachieve the required modulation, especially for an image having a wideFOV, very high resolutions in the order of a few thousands line-pairsper millimeter, are required. As explained above in relation to theholographic displays, this type of high resolution SLM does notpresently exist, and probably will not exist in the foreseeable future.

A possible method for achieving the required Fourier-transform displaysis to use the same method described hereinabove in relation to achievingdynamic holographic-like three-dimensional displays. The requiredmodulation of the SLM plane can be described as an interference patternbetween a simple reference illuminating plane wave and the requiredimage which is collimated to infinity. When an SLM, modulated accordingto this interference pattern, is illuminated by a readout wave which issimilar to the reference wave, the diffracted output light waves will bethe required collimated image. Therefore, the same technique which isillustrated in relation to FIG. 17, can be utilized here to “imitate”the required spatially modulated display, namely, each pixel in thedisplay will emit an assembly of light waves during any given framerate, similar to those that should be diffracted from the SLM plane whenilluminated by the proper readout wave. Eventually, the outcome will bethe same and the output light waves will be the required Fouriertransform of the real image.

In all of the embodiments illustrated in FIGS. 11-17, it was assumedthat the viewer's position is unknown and that the image emitted fromthe display should cover an entire designated FOV, wherein the viewer'seyes can be positioned anywhere inside this FOV. It is possible,however, to further improve the performance and the brightness of theprojected image, as well as to significantly simplify the operation ofthe display, by adding an eyeball tracking unit to the optical system.Eyeball tracking is the process of measuring either the location, thepoint of gaze or the motion of an eye relative to the display, namely,an eyeball tracker is a device for measuring eye positions and eyemovement. The most popular method for operating this device is byutilizing an optical method for measuring eye motion. Light from anemitter, typically infrared, is reflected from the eye and sensed by avideo camera, or some other specially designed optical sensors. Theinformation is then analyzed to extract eye rotation and translationfrom changes in reflections. Video-based eye trackers typically usecorneal reflection and the center of the pupil as features to track overtime.

In accordance with the present invention, it would be advantageous tophysically combine the two optical units, namely, the dynamicallycontrolled stereoscopic display and the eyeball tracking unit. Byidentifying the position and gazing point of the viewer's eyes, thecontrol unit could be set for each pixel at each time frame so that thepreferred direction that the pixel should emit the light wave, and thecontext of the image could be adjusted according to the data received bythe eyeball tracking unit. The display can project different images forthe two eyes of the viewer, to facilitate a stereoscopic image,utilizing the dynamically controlled pixels. Moreover, completelydifferent images can be projected simultaneously by the display todifferent users.

Usually, from symmetry consideration, it would be preferable to installthe eyeball tracking unit at a central top position of the displaymodule. FIGS. 18A-18B illustrate a top view (FIG. 18A) and a front view(FIG. 18B) of an eyeball tracking unit 108, comprising an emitter 109and a detector 110 which are installed at the central top position of aframe of a display module 111. As shown, light rays 112 a and 112 bemerge from the emitter 109 to illuminate the viewer's eyes 114 a and114 b, respectively. The light rays 116 a and 116 b, respectively,reflected from the viewer's eyes, are focused into the detector 110. Thedata collected in the detector 110 is transmitted to a processing unit118, which dynamically calculates the positions, as well as the gazingpoints of the eyes, and accordingly determines the direction that eachpixel should emit the light wave, as well as the context of the image.The processed data is transferred into a control unit 120 which feedsthe display with the processed video signal. This additional capabilitycan enhance the performance of the embodiments illustrated in FIGS.11-17.

FIG. 19 illustrates an upgraded version of the system illustrated inFIGS. 11A-11B above. As illustrated in relation to the later figures,the scanning capability of the DGE-based pixels was degenerated thereonly to a bi-state operation mode. In the modified system illustrated inFIG. 19, however, the full scanning capability has been regenerated.Each pixel can now be, in addition to the “off” state, where thecontrolled refractive index is set to v_(d), deviates the output lightwave by an angle φ_(d), and directs the light wave to the heat sink, ina continuum of states wherein the refractive index v_(b) deviates theoutput light wave by an angle φ_(b). The deviation angle of each pixelis set by the control unit according to the position of the viewer'seyes. The divergence angle Δθ′ of each pixel set by the diffuser 46, cannow be significantly smaller than that of the system illustrated in FIG.11B, where the light wave should cover the entire FOV. As a result, amuch higher brightness, or alternatively, considerably lower powerconsumption may be achieved. There are some alternatives in which themodified embodiment of FIG. 19 can be achieved. In one option, eachpixel is directed to the viewer's head and should cover both eyes. As aresult, a conventional two-dimensional image is projected into theviewer's eyes, but the operation mode is very simple and the improvementin the achievable brightness remains significant. In this option, fewdifferent conventional two-dimensional images can be projectedsimultaneously to the eyes of different users. In a different option, ineach time frame the pixels project the light waves sequentially into thetwo eyes of the viewer. Each time frame is divided into three time slotsfor each pixel: two for the eyes and the third for the heat sink, wherethe duration of each slot is determined according to the brightness ofthe projected light waves. The projected image in this version can bestereoscopic, and since the required light wave divergence is even morereduced, the achievable brightness can be further improved accordingly.In a modified version the pixels array is separated into pairs ofpixels, where in each pair, the two pixels project the light waves intothe two eyes, respectively, namely, each single pixel emits the lightwaves toward a single eye. As shown in FIG. 19, the controlledrefractive indices of the DEGs, DEG₁ and DEG₂ are set to val and vat,which deviate the output light waves by the angles φ_(d1) and φ_(d2)toward the left and the right eyes of the viewer, respectively. Althoughthe resolution for each eye is reduced by a factor of two as compared tothe previous option, controlling the image here is much simpler.

FIG. 20 illustrates a modified version of the embodiment illustrated inFIGS. 14 and 15, wherein the system is designated for a multi-vieweroperation. Assuming that k different viewers are watching the displaysimultaneously, instead of projecting n*m different images in n*m timeslots for each frame time to cover the entire FOV, each pixel emits 2 kdifferent images to 2 k directions in order to cover the 2 k differentEMBs of the k viewers. Since even for a large number k of viewers, thetotal area of all the EMBs is just a small fraction of the entire FOV,the divergence angle Δφ can be significantly smaller than the divergenceangle required for the system of FIG. 15 and the brightness, as well asthe power consumption, can be improved accordingly. Most importantly,since each pixel can continuously follow the eye's movements, the imagecan now be more continuous with higher resolution and a simpler controlmechanism.

FIGS. 21A and 21B illustrate a modified version of the holographicdisplay illustrated in FIG. 17. As shown in FIG. 21A, an eyeballtracking unit 108 is located on the frame of the display 93 and measuresthe position as well as the gaze direction of the eyes 114 a and 114 b.Accordingly, as illustrated in FIG. 21B, each pixel should continuouslyscan the output light wave to create the pattern of the required virtualimage into a solid angle that covers the viewer's eye, which is smallerby a few orders of magnitude than the solid angle required in theembodiment of FIG. 17. As a result, the feasibility of the scanningsystem here is much more realistic and it can now easily be achieved.Moreover, since the gazing direction of each eye is known, only thepixels that the eye looks at should emit a high resolution image,wherein the pixels located further away from the gazing points, can emitimage with lower resolution, even further simplifying the scanningsystem.

The embodiments illustrated in FIGS. 18-21 have some prominentadvantages as compared to those illustrated in FIGS. 11-17. In additionto the significantly higher achievable brightness (or conversely, lowerpower consumption), a much simpler control mechanism and betterfeasibility, there are many applications that can be achieved whencombining the dynamically controlled display with an eyeball trackingunit. Concerning a single-viewer mode, different aspects of a scene canbe projected to the viewer's eyes according to the location, as well asthe gazing point of the viewer's eyes. Moreover, completely differentscenes or different contexts can be projected accordingly. In addition,the viewer can operate the display by blinking his eyes or merelymoving. Furthermore, the system can be programed to change the mode ofoperation according to the situation of the viewer's eyes, for example,pausing the image projection while the viewer turns his head, or startsnapping for more than a preset time period, and renewing it when heturns his gaze back. Regarding a multi-viewer mode, different aspects ofthe same scene (for example, different aspects of the same sport eventor the same show) can be projected simultaneously for different users,according to their specific positions or preferences. In addition, thesystem can pause the projection for one user in one of theabove-mentioned conditions, while continuing to project the images tothe other users. Moreover, completely different scenes for differentusers can be projected simultaneously, for example, a few viewers cansit together while each one watches his own preferred movie or TV show,or a few players can play the same video game, while the system projectshis respective context for each player. Naturally, for the lastmentioned applications, each viewer should use his own headset, in orderto hear the appropriate audio signal.

In addition to the entertainment applications described above, theembodiments of FIGS. 18-21 can also be used for professionalapplications where it is required to continuously project updated datato the viewers' eyes. In a surgery room, for example, there is a largescreen that projects vital data to the medical staff. Different membersof the medical staff, however, i.e., the surgeons, nurses andanesthesiologists, usually require different kinds of data. By utilizingthe above embodiments, it is possible to simultaneously project from thesame screen different data to the various people in the surgery room,according to their different requirements. Another example is a controlroom, wherein a huge screen constantly projects an updated situationreport. Different participants may, however, need to see differentscenarios or different aspects of a given scenario, at any given time.Here again, the different scenarios can simultaneously be projected tothe respective participants, according to their requirements.

It will be evident to those skilled in the art that the invention is notlimited to the details of the foregoing illustrated embodiments and thatthe present invention may be embodied in other specific forms withoutdeparting from the spirit or essential attributes thereof. The presentembodiments are therefore to be considered in all respects asillustrative and not restrictive, the scope of the invention beingindicated by the appended claims rather than by the foregoingdescription, and all changes which come within the meaning and range ofequivalency of the claims are therefore intended to be embraced therein.

What is claimed is:
 1. An optical display system, comprising: a lightsource; a control unit; and at least one juxtaposed double gratingelement, including a first Fresnel element and a second Fresnel element,the elements being spaced apart at a constant distance from each other,each of the two Fresnel elements having a center and at least one edgeand comprising at least one sequence of a plurality of lines, the secondFresnel element being different from the first Fresnel element, thespacings between the lines gradually changing from the center of thegrating to the edge, the sequence of the plurality of lines of at leastone of the Fresnel elements having a radial symmetry, the first Fresnelelement deviating a light wave from the light source towards the secondFresnel element that is further deviated by the second Fresnel elementas an output light wave in a given direction, the direction of theoutput light wave being dynamically and externally controlled by thecontrol unit; wherein for a collimated light source and for eachdeviated direction, the output light wave is a plane wave.
 2. Theoptical display system according to claim 1, wherein for at least one ofthe gratings the distance between two adjacent lines decreases linearlyas a function of the distance from the center.
 3. The optical displaysystem according to claim 1, wherein for each element at least one ofthe two gratings is laterally displaceable, and the direction of theoutput light wave from the second Fresnel element is controlled by alateral displacement of one of the Fresnel elements with respect to theother.
 4. The optical display system according to claim 3, wherein oneof the Fresnel elements is displaceable along two different axes.
 5. Theoptical display system according to claim 4, wherein the direction ofthe output light wave from the second Fresnel element can be deviatedalong two different axes.
 6. The optical display system according toclaim 1 wherein the field-of-view is defined by a solid angle and thedeviated light wave covers the entire solid angle of the field-of-view.7. The optical display system according to claim 1 wherein each of theFresnel elements is characterized by a grating function and for at leastone of the Fresnel elements the grating function is linearlymonotonically increasing as a function of the radius of the element.